Applications of a superconducting device that mixes surface acoustic waves and microwave signals

ABSTRACT

Superconducting device applications implemented with a surface acoustic wave resonator and a superconducting microwave resonator coupled to a Josephson ring modulator are provided. A method can comprise receiving, by a microwave Josephson mixer, and from a superconducting surface acoustic wave resonator of a superconducting device, a surface acoustic wave signal that comprises one or more phonons that resonate at a first frequency. The method can also comprise receiving, by the microwave Josephson mixer and from a superconducting microwave resonator of the superconducting device, a microwave signal that comprises one or more photons that can resonate at a second frequency. Further, the method can also comprise mixing, by the microwave Josephson mixer, the surface acoustic wave signal and the microwave signal based on a microwave control signal received from a microwave source operatively coupled to the microwave Josephson mixer.

BACKGROUND

In quantum circuits, a Josephson ring modulator is coupled to twosuperconducting microwave resonators and three-way mixing is performedbetween differential modes supported by the two superconductingmicrowave resonators and a non-resonant, common drive fed to theJosephson ring modulator. Due to coupling the Josephson ring modulatorto the two superconducting microwave resonators, the device is limitedin the choice of the frequencies of the differential modes, which cancause one or more problems. For example, coupling the Josephson ringmodulator to low-frequency, transmission-line resonators can havevarious problems, such as occupying a large area (e.g., a largefootprint). Another problem is the relatively large linear inductanceassociated with the low resonance-frequency transmission-line comparedto the inductance of the Josephson ring modulator. This can result in avery reduced participation ratio which in turn requires, for itsoperation, very high external quality factors (Qs) for the resonators.However, high external Qs for the resonators is undesirable because itcan give rise to very narrow dynamical bandwidths, which severely limitthe device usability and practicality.

In addition, coupling the Josephson ring modulator to low-frequency,lumped-element resonators can require the use of large lumpedcapacitances and large lumped inductances. Large lumped capacitances andinductances are difficult to realize in practice. Large capacitances canhave considerable loss (lowering the internal Q of the device) and as aresult can cause a considerable portion of the quantum signal to belost. Large geometric inductances usually suffer from parasiticcapacitances which limit their utility. Large kinetic inductancesusually rely on unconventional thin superconductors which are difficultto fabricate and integrate.

SUMMARY

The following presents a summary to provide a basic understanding of oneor more embodiments of the invention. This summary is not intended toidentify key or critical elements, or delineate any scope of theparticular embodiments or any scope of the claims. Its sole purpose isto present concepts in a simplified form as a prelude to the moredetailed description that is presented later. In one or more embodimentsdescribed herein are devices, systems, methods, apparatuses, and/orcomputer program products that mix surface acoustic waves and microwavesignals, facilitate lossless frequency conversion between a surfaceacoustic wave and a microwave signal, is a nondegenerate parametricJosephson amplifier for surface acoustic waves and microwave signals,and entangles a phononic mode and a photonic mode.

According to an embodiment, a method can comprise receiving, by amicrowave Josephson mixer, and from a superconducting surface acousticwave resonator of a superconducting device, a surface acoustic wavesignal that comprises one or more phonons that resonate at a firstfrequency. The method can also comprise receiving, by the microwaveJosephson mixer and from a superconducting microwave resonator of thesuperconducting device, a microwave signal that comprises one or morephotons that can resonate at a second frequency. Further, the method canalso comprise mixing, by the microwave Josephson mixer, the surfaceacoustic wave signal and the microwave signal based on a microwavecontrol signal received from a microwave source operatively coupled tothe microwave Josephson mixer. An advantage of such a method is thatdissipationless, three-wave mixing and amplification can be performedbetween low microwave frequencies of the superconducting surfaceacoustic wave resonator and high microwave frequencies of thesuperconducting microwave resonator. Another advantage is that quantuminformation carried by a surface acoustic wave signal can be transducedinto a microwave signal or vice versa in a unitary manner (e.g., theenergy and phase coherence of the quantum signal are preserved). Also,this quantum operation can be controlled and enabled by a separatemicrowave control signal (referred to as the pump or pump device)received by the device.

In some implementations, the method can comprise transferring, by themicrowave Josephson mixer, quantum information from the superconductingsurface acoustic wave resonator to the superconducting microwaveresonator (and/or from the superconducting microwave resonator to thesurface acoustic wave resonator) based on an application of pump driveapplied at a frequency difference between the microwave signal and thesurface acoustic wave signal. An advantage of such a method is that themicrowave control signal can be utilized to select the modes whoseinformation is swapped or transduced.

In some implementations, the method can advantageously comprisedisconnecting, by the microwave Josephson mixer, a connection orinteraction between the superconducting surface acoustic wave resonatorand the superconducting microwave resonator based on determining thatthe mixing of the surface acoustic wave signal and the microwave signalis to be stopped. Further, the method can comprise reenabling, by themicrowave Josephson mixer, the connection or interaction between thesuperconducting surface acoustic wave resonator and the superconductingmicrowave resonator based on determining that the mixing of the surfaceacoustic wave signal and the microwave signal is to be restarted. Anadvantage of such a method is that the microwave Josephson mixer cancontrol transfer of information between the surface acoustic wave signaland the microwave signal.

According to some implementations, the method can comprise transferring,by the microwave Josephson mixer, a first portion of quantum informationbetween the superconducting surface acoustic wave resonator and thesuperconducting microwave resonator based on a first power of themicrowave control signal. The method can also comprise transferring, bythe microwave Josephson mixer, a second portion of quantum informationbetween the superconducting surface acoustic wave resonator and thesuperconducting microwave resonator based on a second power of themicrowave control signal. An advantage of such a method is that anamount of information transferred can be controlled by the microwaveJosephson mixer and the power of the microwave control signal.

Another embodiment relates to a method that can comprise receiving, at afrequency converter, and from a superconducting surface acoustic waveresonator, a surface acoustic wave signal that comprises one or morephonons that resonate at a first frequency. The method can also comprisereceiving, at the frequency converter and from a superconductingmicrowave resonator, a microwave signal that comprises one or morephotons that resonate at a second frequency. Further, the method cancomprise implementing, by the frequency converter, a lossless frequencyconversion between first information of the superconducting surfaceacoustic wave resonator and second information of the superconductingmicrowave resonator based on a pump signal received from a microwavesource. An advantage of such a method is that the conversion between thesurface acoustic wave and the microwave signal is a lossless frequencyconversion.

According to some implementations, the method can comprise mapping, bythe frequency converter, a propagating radio frequency signal to aphononic mode in the superconducting surface acoustic wave resonator.Further, the method can comprise upconverting, by the frequencyconverter, the phononic mode to a photonic mode in the superconductingmicrowave resonator via an application of a microwave control signal(e.g., pump) with a defined frequency. Upconverting the phononic modecan be enabled by a lossless three-wave mixing interaction. Anupconverted microwave signal propagates upon leaving the superconductingmicrowave resonator. An advantage of such a method is that a propagatingphonon mode or low-frequency microwave signal can be upconverted to apropagating photonic mode (e.g., high-frequency microwave mode) via alossless three-wave mixing interaction.

Alternatively, the method can comprise mapping, by the frequencyconverter, a propagating microwave signal to a photonic mode in thesuperconducting microwave resonator. Further, the method can comprisedownconverting, by the frequency converter, the photonic mode to aphononic mode in the superconducting surface acoustic wave resonator viaan application of a microwave control signal (e.g. the pump) with adefined frequency. Downconverting the photonic mode can be enabled by alossless three-wave mixing interaction. Further, a downconverted surfaceacoustic wave signal can propagate upon leaving the superconductingsurface acoustic wave resonator. An advantage of such a method is that apropagating photonic mode (e.g., high-frequency microwave mode) can bedownconverted to a propagating phononic mode or low-frequency microwavemode via a lossless three-wave mixing interaction.

In accordance with another embodiment, provided is a method that cancomprise amplifying, by a Josephson parametric amplifier, firstquadratures of a surface acoustic wave signal entering a first port of adevice and second quadratures of a microwave signal entering a secondport of the device. Further, the method can comprise outputting, by theJosephson parametric amplifier, and through an output port, a firstamplified signal that comprises a first reflective signal and a firsttransmitted signal with frequency conversion and a second amplifiedsignal that comprises a second reflective signal and a secondtransmitted signal with frequency conversion. An advantage of such amethod is that the method can function as a phase-preservingquantum-limited amplifier for low-frequency and high-frequency microwavesignals.

In another embodiment, provided is a method that can comprise inputting,by an entanglement component, a first input signal that comprises afirst frequency into a superconducting surface acoustic wave resonator.A first qubit is operatively coupled to the entanglement component viathe superconducting surface acoustic wave resonator. The method can alsocomprise inputting, by the entanglement component a second input signalthat comprises a second frequency into a superconducting microwaveresonator. A second qubit is operatively coupled to the entanglementcomponent via the superconducting microwave resonator. The method canalso comprise outputting, by the entanglement component, an outputsignal that comprises an amplified superposition of input fieldsentering the superconducting surface acoustic wave resonator and thesuperconducting microwave resonator. An advantage of such a method isthat the entanglement can be between a phononic mode and a photonicmode.

A further embodiment relates to a superconducting device that cancomprise a first superconducting qubit capacitively coupled to asuperconducting surface acoustic wave resonator and a secondsuperconducting qubit capacitively coupled to a superconductingmicrowave resonator. The superconducting device can also comprise aJosephson ring modulator coupled to the superconducting surface acousticwave resonator and the superconducting microwave resonator. An advantageof such a superconducting device is that the device can be operate as anondegenerate amplifier and entanglement can be generated between thequbits via entanglement of the phonons supported by the superconductingsurface acoustic wave resonator and photons supported by thesuperconducting microwave resonator.

DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates an example, non-limiting block diagram of a circuitcomprising the Josephson ring modulator in accordance with one or moreembodiments described herein.

FIG. 2 illustrates an example, non-limiting block diagram of a circuitcomprising a superconducting surface acoustic wave resonator inaccordance with one or more embodiments described herein.

FIG. 3 illustrates an example, non-limiting, schematic of a circuit fora superconducting device that comprises a surface acoustic waveresonator and superconducting microwave resonator coupled to a Josephsonring modulator in accordance with one or more embodiments describedherein.

FIG. 4 illustrates an example, non-limiting schematic representation ofa system that comprises a unitary Josephson mixer for surface acousticwaves (phonons) and microwave signals (photons) in accordance with oneor more embodiments described herein.

FIG. 5 illustrates an example, non-limiting schematic representation ofa system that comprises a lossless frequency converter between a surfaceacoustic wave and a microwave signal in accordance with one or moreembodiments described herein.

FIG. 6 illustrates an example, non-limiting schematic representation ofa system that comprises a nondegenerate parametric Josephson amplifierfor surface acoustic waves and microwave signals in accordance with oneor more embodiments described herein.

FIG. 7 illustrates an example, non-limiting schematic representation ofa system that comprises an entangler of a phononic mode and a photonicmode in accordance with one or more embodiments described herein.

FIG. 8 illustrates a flow diagram of an example, non-limiting, methodfor mixing surface acoustic waves (phonons) and microwave signals(photons) in accordance with one or more embodiments described herein.

FIG. 9 illustrates a flow diagram of an example, non-limiting, methodfor mixing surface acoustic waves and microwave signals based on afrequency of a microwave control signal in accordance with one or moreembodiments described herein.

FIG. 10 illustrates a flow diagram of an example, non-limiting, methodfor operations of a switch utilized to mix surface acoustic waves andmicrowave signals based on a frequency and amplitude of a microwavecontrol signal in accordance with one or more embodiments describedherein.

FIG. 11 illustrates a flow diagram of an example, non-limiting, methodfor mixing surface acoustic waves and microwave signals based on anamplitude of a microwave signal in accordance with one or moreembodiments described herein.

FIG. 12 illustrates a flow diagram of an example, non-limiting, methodfor a lossless frequency conversion between a surface acoustic wave anda microwave signal in accordance with one or more embodiments describedherein.

FIG. 13 illustrates a flow diagram of an example, non-limiting, methodfor performing an up-conversion from a surface acoustic wave signal to amicrowave signal in accordance with one or more embodiments describedherein.

FIG. 14 illustrates a flow diagram of an example, non-limiting, methodfor performing a down-conversion from a microwave signal to a surfaceacoustic wave signal in accordance with one or more embodimentsdescribed herein.

FIG. 15 illustrates a flow diagram of an example, non-limiting, methodfor performing nondegenerate parametric amplification for surfaceacoustic waves and microwave signals in accordance with one or moreembodiments described herein.

FIG. 16 illustrates a flow diagram of an example, non-limiting, methodfor entangling a phononic mode and a photonic mode of a quantum circuitin accordance with one or more embodiments described herein.

FIG. 17 illustrates a block diagram of an example, non-limitingoperating environment in which one or more embodiments described hereincan be facilitated.

DETAILED DESCRIPTION

The following detailed description is merely illustrative and is notintended to limit embodiments and/or application or uses of embodiments.Furthermore, there is no intention to be bound by any expressed orimplied information presented in the preceding Background or Summarysections, or in the Detailed Description section.

One or more embodiments are now described with reference to thedrawings, wherein like referenced numerals are used to refer to likeelements throughout. In the following description, for purposes ofexplanation, numerous specific details are set forth in order to providea more thorough understanding of the one or more embodiments. It isevident, however, in various cases, that the one or more embodiments canbe practiced without these specific details.

As it relates to circuits, and more specifically quantum circuits, if aJosephson ring modulator (JRM) is coupled to two superconducting waveresonators, there is a limitation with respect to the choice ofdifferential modes. For example, a problem associated with coupling theJRM to low-frequency, transmission-line resonators is that a large areais occupied by the device. As another example, a problem associated withcoupling a JRM to low frequency lumped-element resonators is that largecapacitors are relatively lossy. A solution provided by thesuperconducting device, the superconducting circuit, and the methodsdiscussed herein is that a superconducting surface acoustic waveresonator is utilized, which is compact and, therefore, a size and/or aloss of the superconducting device can be reduced.

Another problem associated with prior art superconducting devices (e.g.,devices that utilize two superconducting microwave resonators) is thatthe prior art superconducting devices are limited to mixing frequenciesbetween 5 Gigahertz (GHz) and 15 GHz. The various superconductingdevices, circuits, and methods discussed herein provide a solution tothis problem through the utilization of a superconducting surfaceacoustic wave resonator and superconducting wave resonator that enabledissipationless, three-wave mixing and amplification between lowmicrowave frequencies (e.g., about 0.1 GHz to about 4 GHz) and highmicrowave frequencies (e.g., around 5 GHz to around 15 GHz).

Given the above problems with prior art superconducting devices, thevarious aspects provided herein can be implemented to produce a solutionto one or more of these problems in the form of a superconductingdevice, superconducting circuit, and method of fabricating the same.Such systems, devices, circuits, methods, and/or computer programproducts implementing such a superconducting device can have anadvantage of reduced size and low-loss resonators, as compared toconventional techniques.

According to some implementations, the device can function as aJosephson mixer between surface acoustic waves (phonons) and microwavesignals (photons). Additionally, or alternatively, the device canfunction as a lossless frequency converter between a surface acousticwave and a microwave signal. Additionally, or alternatively, the devicecan function as a nondegenerate parametric Josephson amplifier for asurface acoustic wave and a microwave signal. In additional oralternative implementations, the device can function as an entangler ofa phononic mode and photonic mode.

FIG. 1 illustrates an example, non-limiting block diagram of a circuit100 in accordance with one or more embodiments described herein. Thecircuit 100 can comprise a superconducting surface acoustic wave (SAW)resonator (referred to as a superconducting SAW resonator 102), asuperconducting microwave resonator 104, and a Josephson ring modulator(referred to as a JRM 106).

In a piece of quantum hardware, which includes the superconductingqubits space, a mechanism to implement gate operations or measurementson the quantum hardware is to generate microwave signals or receivemicrowave signals by the superconducting SAW resonator 102 and/or viathe superconducting microwave resonator 104. As discussed herein,according to some implementations, the circuit 100 can operate as aJosephson mixer between surface acoustic waves (phonons) and microwavesignals (photons). Further, the circuit 100 can operate as a losslessfrequency converter between a surface acoustic wave and a microwavesignal. In some implementations, the circuit 100 can operate as anondegenerate parametric Josephson amplifier for a surface acoustic waveand a microwave signal. In additional and/or alternate implementations,the device can operate as an entangler of a phononic mode and photonicmode.

SAW resonators (e.g., the superconducting SAW resonator 102) areelectro-mechanical resonators for phonons, which can resonate atmicrowave frequencies of around 0.5 GHz to 5 GHz. Surface acoustic waveresonators (or surface acoustic wave filters) are used in manytelecommunication applications (e.g., mobile phones). SAW resonators canalso be useful in quantum computing applications and quantum circuits inthe microwave domain, as discussed herein. Further, surface acousticwave resonators can have high internal Quality (Q) factors, which can bein excess of 10⁵. Therefore, SAW resonators can have a very low loss. Inaddition, SAW resonators are very compact. For example, the surfaceacoustic resonance wavelengths are very short (e.g., less than 1 micrometre or <1 μm).

The superconducting SAW resonator 102 can be a low frequency device andthe superconducting microwave resonator 104 can be a high frequencydevice. Further, the superconducting SAW resonator 102 can beimplemented on a low-loss piezo-electric dielectric substrate. Thelow-loss piezo-electric dielectric substrate can comprise a materialselected from a group of materials comprising quartz, gallium arsenide,lithium niobite, and/or zinc oxide, or the like. The superconductingmicrowave resonator 104 can be implemented using lumped-elementcapacitance and lumped-element inductance. Further details related tothe superconducting SAW resonator 102 and the superconducting microwaveresonator 104 will be provided below with respect to FIGS. 2 and 3.

The JRM 106 is a device that can be based on Josephson tunnel junctions.For example, the JRM 106 can comprise one or more Josephson junctionsarranged in a Wheatstone-bridge configuration. The one or more Josephsonjunctions can comprise a material selected from a group of materialscomprising aluminum and niobium. Further, the JRM 106 can performnon-degenerate mixing in the microwave regime, without losses. Accordingto some implementations, the JRM 106 can be a dispersive nonlinearthree-wave mixing element.

The JRM 106 can support two differential modes and two common modes (oneof which is at zero frequency, and, therefore, not applicable to the oneor more embodiments described herein). By coupling the JRM 106 to asuitable electromagnetic environment (which supports two differentialmicrowave modes), the circuit 100 can be used to perform various quantumprocessing operations such as lossless frequency conversion in themicrowave domain, parametric amplification at the quantum limit (e.g.,amplification of quantum signals in the microwave domain), and/orgeneration of two-mode squeezing.

The Josephson ring modulator (e.g., the JRM 106) can comprise one ormore Josephson junctions arranged in a Wheatstone-bridge configuration.The Josephson junctions are illustrated as a first Josephson junction108, a second Josephson junction 110, a third Josephson junction 112,and a fourth Josephson junction 114. The Josephson junctions (e.g., thefirst Josephson junction 108, the second Josephson junction 110, thethird Josephson junction 112, the fourth Josephson junction 114) can beformed in a loop. Further, the Josephson junctions can be utilized toperform the mixing as discussed herein.

The JRM 106 also can comprise four additional junctions (internal to theloop), which can be shunt junctions according to some implementations.These four additional junctions are labeled as a first internal junction116, a second internal junction 118, a third internal junction 120, anda fourth internal junction 122. The four internal junctions (e.g., thefirst internal junction 116, the second internal junction 118, the thirdinternal junction 120, and the fourth internal junction 122) canfacilitate tuning of the frequency of the circuit 100. The tunabilitycan be obtained with the application of external magnetic flux. In thisconfiguration, the four internal junctions, which are larger than thejunctions on the outer loop, can function as linear inductors shuntingthe outer Josephson junctions. By threading external flux through theinner loops, the total inductance of the JRM 106 can change, which canlead to a change in the resonance frequencies of the resonators coupledto the JRM 106.

In addition, the configuration of the JRM 106 defines points or nodeswhere the external junctions meet. Accordingly, there can be a firstnode 124 at the bottom of the JRM 106; a second node 126 at the rightside of the JRM 106; a third node 128 at the top of the JRM 106; and afourth node 130 at the left side of the JRM 106. It is noted that theterms bottom, right side, top, and left side are for purposes ofexplaining the disclosed aspects with respect to the figures and thedisclosed aspects are not limited to any particular plane or orientationof the JRM 106 and/or the circuit 100 and its associated circuitry.

The four nodes (e.g., the first node 124, the second node 126, the thirdnode 128, and the fourth node 130) can be utilized to define thedifferential mode and the common mode hosted by the circuit 100. Themodes can be orthogonal and do not overlap one another. Further, thenodes, as illustrated, can be physically orthogonal. For example, thefirst node 124 and the third node 128 are vertical to one another andthe second node 126 and the fourth node 130 are horizontal to oneanother.

The nodes can be utilized to couple the JRM 106 to the superconductingSAW resonator 102 and to the superconducting microwave resonator 104.For example, a first set of opposite nodes (e.g., the first node 124 andthe third node 128) can be chosen to operatively couple the JRM 106 tothe superconducting SAW resonator 102. The first node 124 can be coupledto the superconducting SAW resonator 102 via a first wire 132 (or firstlead) and the third node 128 can be coupled to the superconducting SAWresonator 102 via a second wire 134 (or second lead).

The second set of opposite nodes (e.g., the second node 126 and thefourth node 130) can be chosen to operatively couple the JRM 106 to thesuperconducting microwave resonator 104. For example, the second node126 can be coupled to the superconducting microwave resonator 104 via athird wire 136 (or third lead) and the fourth node 130 can be coupled tothe superconducting microwave resonator 104 via a fourth wire 138 (orfourth lead).

As illustrated, the first wire 132 and the second wire 134 can becoupled to the superconducting SAW resonator 102 at different locationsof the superconducting SAW resonator 102. Further, the third wire 136and the fourth wire 138 can be coupled to the superconducting microwaveresonator 104 at different locations of the superconducting microwaveresonator 104. Further details related to the coupling locations will beprovided below with respect to FIG. 3.

The superconducting SAW resonator 102, the superconducting microwaveresonator 104, and the JRM 106 are portions of afrequency-converter/mixer/amplifier/entangler device. The device canreceive external microwave photons or phonons from other quantum devicesconnected to the microwave port and/or the SAW port of the device.

The circuit 100, as well as other aspects discussed herein can beutilized in a device that facilitates manipulation of quantuminformation in accordance with one or more embodiments described herein.Aspects of devices (e.g., the circuit 100 and the like), systems,apparatuses, or processes explained in this disclosure can constitutemachine-executable component(s) embodied within machine(s), e.g.,embodied in one or more computer readable mediums (or media) associatedwith one or more machines. Such component(s), when executed by the oneor more machines, e.g., computer(s), computing device(s), virtualmachine(s), etc. can cause the machine(s) to perform the operationsdescribed.

In various embodiments, the device can be any type of component,machine, system, device, facility, apparatus, and/or instrument thatcomprises a processor and/or can be capable of effective and/oroperative communication with a wired and/or wireless network.Components, machines, apparatuses, systems, devices, facilities, and/orinstrumentalities that can comprise the device can include tabletcomputing devices, handheld devices, server class computing machinesand/or databases, laptop computers, notebook computers, desktopcomputers, cell phones, smart phones, consumer appliances and/orinstrumentation, industrial and/or commercial devices, hand-helddevices, digital assistants, multimedia Internet enabled phones,multimedia players, and the like.

In various embodiments, the device can be a quantum computing device orquantum computing system associated with technologies such as, but notlimited to, quantum circuit technologies, quantum processortechnologies, quantum computing technologies, artificial intelligencetechnologies, medicine and materials technologies, supply chain andlogistics technologies, financial services technologies, and/or otherdigital technologies. The circuit 100 can employ hardware and/orsoftware to solve problems that are highly technical in nature, that arenot abstract and that cannot be performed as a set of mental acts by ahuman. Further, in certain embodiments, some of the processes performedcan be performed by one or more specialized computers (e.g., one or morespecialized processing units, a specialized computer with a quantumcomputing component, etc.) to carry out defined tasks related to machinelearning.

The device and/or components of the device can be employed to solve newproblems that arise through advancements in technologies mentionedabove, computer architecture, and/or the like. One or more embodimentsof the device can provide technical improvements to quantum computingsystems, quantum circuit systems, quantum processor systems, artificialintelligence systems and/or other systems. One or more embodiments ofthe circuit 100 can also provide technical improvements to a quantumprocessor (e.g., a superconducting quantum processor) by improvingprocessing performance of the quantum processor, improving processingefficiency of the quantum processor, improving processingcharacteristics of the quantum processor, improving timingcharacteristics of the quantum processor, and/or improving powerefficiency of the quantum processor.

FIG. 2 illustrates an example, non-limiting block diagram of a circuit200 comprising a superconducting surface acoustic wave (SAW) resonatorin accordance with one or more embodiments described herein. Repetitivedescription of like elements employed in other embodiments describedherein is omitted for sake of brevity.

The superconducting SAW resonator 102 can comprise a firstsuperconducting metallic/dielectric mirror (e.g., a first Bragg mirror202) and a second superconducting metallic/dielectric mirror (e.g., asecond Bragg mirror 204). The first Bragg mirror 202 can be separatedfrom the second Bragg mirror 204 by a distance that is an odd integermultiple of a half-wavelength supported by the superconducting SAWresonator 102. A Bragg mirror comprises a periodic structure of metallicfingers and dielectric gaps positioned at a defined distance from oneanother.

According to some implementations, the superconducting SAW resonator 102can be attached to (e.g., realized on) a low-loss piezo-electricdielectric substrate (not shown). The low-loss piezo-electric dielectricsubstrate can comprise a material selected from a group of materialscomprising one or more of quartz, gallium arsenide, lithium niobite, andzinc oxide, or a similar material.

Further, a first interdigitated capacitance device or first IDC device206 and a second IDC device 208 can be included. The first IDC device206 can couple between the superconducting SAW resonator 102 and the JRM106. The second IDC device 208 can couple between the superconductingSAW resonator 102 and an external port (e.g., a signal port 212).

For example, the first IDC device 206 can be positioned at a center ofthe superconducting SAW resonator 102. A first set of opposite nodes ofthe JRM 106 can be connected to opposite nodes of the first IDC device206. For example, the first node 124 of the JRM 106 can be connected toa first side of the first IDC device 206 (e.g., via the first wire 132).Further, the third node 128 of the JRM 106 can be connected to a secondside of the first IDC device 206 (e.g., via the second wire 134).

A second set of opposite nodes of the Josephson ring modulator can beconnected to the superconducting microwave resonator 104. For example,the second node 126 of the JRM 106 can be connected to a first side ofthe superconducting microwave resonator 104 (e.g., via the third wire136). Further, the fourth node 130 of the JRM 106 can be connected to asecond side of the superconducting microwave resonator 104 (e.g., viathe fourth wire 138).

The circuit 100 can also comprise a first external feedline 210 coupledto the superconducting SAW resonator 102 through the second IDC device208. The first external feedline 210 can be connected to a signal port212 (e.g., a radio frequency (rf) source). The first external feedline210 can carry one or more input signals and one or more output signalsof the superconducting SAW resonator 102.

A second external feedline 214 can be coupled to the superconductingmicrowave resonator 104. The second external feedline 214 can beconnected to an idler port 216 (e.g., a microwave source). The secondexternal feedline 214 can carry one or more input signals and one ormore output signals of the superconducting microwave resonator 104.

Further, the JRM 106 can be operative connected to a pump port 218(e.g., via the second wire 134 or another wire). The pump port 218 canbe connect to a microwave source. The pump port 218 can supply therequired energy for the operation of the circuit 100. For example, uponor after pump power is supplied from the pump port 218 to the JRM 106,the superconducting SAW resonator 102 and the superconducting microwaveresonator 104 can be electrically connected through the JRM 106.However, when power is not supplied through the pump port 218 (e.g., thepower supply is off), the superconducting SAW resonator 102 and thesuperconducting microwave resonator 104 can be electrically isolatedfrom one another.

For amplification, ideally there would be a microwave signal that ispropagating on the idler transmission line (e.g., the second externalfeedline 214) that is connected to the idler port 216. In an example,assume that the microwave signal is weak and it carries some quantuminformation that is of value. The information goes into the circuit 100and there is a pump tone that is fed to the device (e.g., via the pumpport 218) that can generate a parametric amplification between the idlermode and the signal mode supported by the superconducting SAW resonator102. In this example, an input signal is not needed at both the signalport 212 and the idler port 216. Instead, a signal is only needed on oneport and quantum noise can enter through the other port. Thedeterministic signal carrying quantum information and the quantum noisecan be mixed by the device via the pump drive and amplified upon leavingthe device. Thus, the signal that carries information can come eitherfrom the signal port 212, or the idler port 216, or can have two signalscarrying information entering both ports at substantially the same time.For simplicity, assume the signal is entering the circuit 100 throughone port and the other port is only receiving quantum noise. In thiscase, through the interaction with the pump (e.g., the pump port 218)and the JRM 106 three-wave mixing takes place between the common mode(pump) and two differential modes (the idler and the signal). If thepump frequency is the sum of the signal and idler resonance frequencies,the device functions as a phase-preserving parametric amplifieroperating near the quantum limit. The respective output signal exitingthe signal port 212 and idler port 216 can be an amplified superpositionof the input signals entering both ports (e.g., the signal port 212 andidler port 216).

According to some implementations, magnetic flux threading the JRM 106can be induced through the one or more external superconducting magneticcoils. For example, magnetic flux threading the JRM 106 can be inducedusing external superconducting magnetic coils attached to a devicepackage or using on-chip flux lines.

In further detail, FIG. 3 illustrates an example, non-limiting,schematic of a circuit 300 for a superconducting device that comprises asurface acoustic wave resonator and superconducting microwave resonatorcoupled to a Josephson ring modulator in accordance with one or moreembodiments described herein. Repetitive description of like elementsemployed in other embodiments described herein is omitted for sake ofbrevity.

It is noted that the Josephson junctions and the four internal junctionsof the JRM 106 are not labeled in FIG. 3 for purposes of simplicity.However, the element numbering of the junctions for purposes ofexplanation are the same as the labeling of FIGS. 1 and 2. In addition,the circuit 300 and its associated components can be implemented on asingle chip, according to some implementations.

As mentioned, the nodes of the JRM 106 can comprise a first set ofopposite nodes that can be oriented in a vertical direction to oneanother. For example, the first set of opposite nodes can comprise thefirst node 124 and the third node 128, which can operatively couple theJRM 106 to the superconducting SAW resonator 102 (e.g., via the firstwire 132 and the second wire 134). Further, the nodes of the JRM 106 cancomprise a second set of opposite nodes, which can be oriented in ahorizontal manner. For example, the second set of opposite nodes cancomprise the second node 126 and the fourth node 130, which canoperatively couple the JRM 106 to the superconducting microwaveresonator 104. It is noted that although illustrated and described withrespect to a horizontal direction and/or a vertical direction, thedisclosed aspects are not limited to this orientation and otherorientations can be utilized.

The first set of opposite nodes (e.g., the first node 124 and the thirdnode 128) can be coupled to opposite electrodes of a firstinterdigitated capacitor or first IDC 302 (e.g., the first IDC device206) of the superconducting SAW resonator 102, creating a firstorthogonal mode. For example, the first node 124 of the JRM 106 can becoupled to a first electrode of the first IDC 302, indicated at 304.Further, the third node 128 of the JRM 106 can be coupled to a secondelectrode of the first IDC 302, indicated at 306. The first IDC 302 canbe positioned at a center of the superconducting SAW resonator 102.

The second set of opposite nodes (e.g., the second node 126 and thefourth node 130) can be coupled to a second capacitor 310 (e.g., ashunting capacitor) forming a superconducting microwave resonator 104,where the JRM is the inductive element of the resonator. Thesuperconducting microwave resonator can support a second orthogonaldifferential mode of the JRM 106. The capacitance (e.g., the firstcapacitor 308) functions as a coupling capacitor between the microwaveresonator (formed by the JRM 106 and the second capacitor 310) and theexternal feedline/port (e.g., the idler port 216) of the device.According to some implementations, the first capacitor 308 and thesecond capacitor 310 can be respective capacitors chosen from a group ofcapacitors comprising a gap capacitor, an interdigitated capacitor,and/or a plate capacitor. In the case of plate capacitance, thedielectric material should have very low-loss at the level of singlemicrowave photons.

As illustrated, the superconducting SAW resonator 102 can comprise thefirst IDC 302, a second IDC 312 (e.g., the second IDC device 208), and aset of metallic/dielectric mirrors (e.g., the first Bragg mirror 202 andthe second Bragg mirror 204). The components of the superconducting SAWresonator 102 (e.g., the first IDC 302, the second IDC 312, the firstBragg mirror 202, the second Bragg mirror 204) is implemented on apiezo-electric substrate. For example, the piezo electric substrate cancomprise one or more of quartz, gallium arsenide, lithium niobite, zincoxide, and/or similar materials.

Different ports can be utilized to access the superconducting SAWresonator 102 and the superconducting microwave resonator 104. Forexample, the signal port 212 can be utilized to access thesuperconducting SAW resonator 102 and the idler port 216 can be utilizedto access the superconducting microwave resonator 104.

The signal port 212 can be utilized to carry input signals and outputsignals. Therefore, in order to measure output signals from thesuperconducting SAW resonator 102, an IDC (e.g., the second IDC device208) can be placed between the first Bragg mirror 202 and the secondBragg mirror 204. One set of IDC fingers that are connected together arelocated at an rf-voltage anti-node (maximum/minimum) of the supportedphononic mode. Therefore, the spacing between the fingers can bedetermined by the wavelength supported by the superconducting SAWresonator 102.

A distance between the centers of two consecutive fingers of the IDCs(e.g., the first IDC 302 and the second IDC 312) can be generallyexpressed as λ_(a)/2. The respective two sets of fingers of the IDCs canhave opposite polarity according to an implementation. Further, thefirst Bragg mirror 202 and the second Bragg mirror 204 can be separatedfrom one other, as indicated by line 314, by a distance that is an oddinteger multiple of half-wavelength supported by the superconducting SAWresonator 102. The defined distance can be expressed as L_(a), whereinL_(a) is an odd-integer multiple of λ_(a)/2. Where λ_(b)<λ_(a).

A microwave tone is characterized by a wave that has a maximum amplitudeand a minimum amplitude. The minimum amplitude should couple to onefinger of the IDC (e.g., indicated at 304 or 306) and the maximum valueshould couple to the other finger, (e.g., indicated at 304 or 306) wherethe two fingers are connected to opposite nodes of the JRM 106 (e.g.,the first node 124 and the third node 128). Therefore, the distanceλ_(a)/2 can be selected to facilitate the maximum on the first fingerand the minimum on the other finger.

Further, for purposes of explanation, the maximum amplitude has a plussign (or a positive value) and the minimum amplitude has a minus sign(or a negative value). Therefore, the two opposite nodes of the JRM 106can be excited by the positive (on the first finger) and the negativerf-voltages (on the second finger). These signals can alternate withtime. However, they should be opposite to one another at any given time.When the polarity is different, it can be referred to as a differentialmode (where differential means opposite sign).

This can also apply to the case of the superconducting microwaveresonator 104. As mentioned, the superconducting microwave resonator cancomprise a first capacitor 308 coupling the resonator to the externalport (e.g., the idler port 216) and the second capacitor 310 shuntingthe JRM 106. The two electrodes of the capacitor shunting the JRM 106(e.g., the second capacitor 310) can have opposite voltages and canexcite a second differential mode. Accordingly, a first differentialmode of the JRM 106 is supported by the superconducting SAW resonator102 and a second differential mode of the JRM 106 is supported by thesuperconducting microwave resonator 104.

Further, in order to perform the mixing, or the amplification, microwaveenergy is supplied for device operation. The energy source for themixing and/or amplification is supplied through the pump port 218. Thepump port 218 can provide a microwave signal, which can be a strong,coherent non-resonant microwave tone that can supply energy for thecircuit 100 to operate. According to some implementations, the microwavesignal supplied by the pump port 218 can comprise a frequency thatsatisfies a defined equation determined based on the energy conservationof the three-wave mixing occurring in the circuit 100.

In an example of amplification performed by the device, a first signalf_(a) which lies within the bandwidth of the superconducting SAWresonator 102 and a second signal f_(b) which lies within the bandwidthof the superconducting microwave resonator 104. Further, the frequencyof the second signal can be larger than the frequency of the firstsignal (f_(b)>f_(a)). To amplify both signals, the frequency of the pumptone fed through the pump port 218 should be the sum of the first signaland the second signal (e.g., f_(a)+f_(b)). The energy of theelectromagnetic signal is proportional to its frequency. By taking thepump (e.g., the pump port 218) frequency to be the sum, if the pumpinteracts with the dispersive nonlinear medium (e.g., the JRM 106), adownconversion process can occur where the energetic photons of the pumpsplit into a first set of photons at f_(a) and a second set of photonsat f_(b). If the frequency is the sum, then the photons can split inthis manner. For example, the photons can split into two halves: a firsthalf (e.g., the first set of photons) at the lower frequency f_(a) and asecond half (e.g., the second set of photons) at the higher frequencyf_(b). Therefore, amplification can occur because the pump exchangesenergy with the signal mode and idler mode and through this exchangeentangled photons are generated in both modes. Similarly, a conversionprocess with non phonon-photon gain can convert one mode to the other(e.g., a photon to a phonon or a phonon to a photon). In this case, thepump frequency should be equal to the difference between f_(a) andf_(b). Here f_(b) is larger, so the equation can be f_(b) minus f_(a).

According to an implementation, in the mixing process (conversionwithout photon-phonon gain) a phonon in the SAW resonator at the signalfrequency can be upconverted into a microwave photon in the microwaveresonator at the idler frequency. According to another implementation,the photon in the microwave resonator at the idler frequency can bedownconverted to a phonon in the SAW resonator at the signal frequency.The energy exchange is enabled by the pump drive (e.g., fed through thepump port 218). Accordingly, either a pump photon is emitted or a pumpphoton is absorbed to facilitate the process.

If there is no pump signal applied to the pump port 218, thesuperconducting SAW resonator 102 and the superconducting microwaveresonator 104 are separated (e.g., isolated from one another) andinformation exchange or information communications between thesuperconducting SAW resonator 102 and the superconducting microwaveresonator 104 does not occur. Upon or after a pump signal is applied tothe pump port 218, it excites the common mode of the JRM 106, asillustrated in FIG. 2, the superconducting SAW resonator 102 and thesuperconducting microwave resonator 104 interact and information isexchanged.

According to some implementations, the pump drive is fed through thesigma port of a 180-degree hybrid 316, which is capacitively coupled toopposite nodes of the JRM 106, which in turn excites a common-mode ofthe JRM 106. According to some implementations, the 180-degree hybrid316 operates as a power splitter.

By way of explanation and not limitation, a 180-degree hybrid is apassive microwave component that comprises four ports. A first port isreferred to as a sum port 318 (or sigma port). If a signal is input tothe sum port 318, the signal splits equally between two other ports(e.g., a second port 320 and a third port 322). The signals that areoutput from the second port 320 and the third port 322 can have the samephase. Thus, the first port is referred to as the sum port 318 becausethe phases of the split signals are equal. The pump drive (e.g., thepump port 218) can be fed through the sum port 318 of the 180-degreehybrid 316.

A fourth port can be referred to as a delta port 324 (or a differenceport). If a signal is injected through the delta port 324 of the180-degree hybrid (which, in FIG. 3, is terminated with 50 ohms), thehybrid would split the signal into two signals, coming out of the twoports (e.g., the second port 320 and the third port 322), but the splitsignals have a 180-degree phase difference. For example, if a firstsignal has a maximum value at one port (e.g., 320), the second signal atthe other port (e.g., 322) has a minimum value. The pump port 218 can befed through the sum port 318.

Also illustrated are a first lead 326 coming out of the second port 320and a second lead 328 coming out of the third port 322. The signals thatare output at the second port 320 and the third port 322 are half of thepump signal and have the same phase, as discussed above. The signalsencounter small coupling capacitors (e.g., a first coupling capacitor330 and a second coupling capacitor 332) that can be coupled to twoopposite nodes of the JRM 106. According to some implementations, thefirst coupling capacitor 330 and the second coupling capacitor 332 canbe respective capacitors chosen from a group of capacitors comprising agap capacitor, an interdigitated capacitor, and a plate capacitor. As itrelates to plate capacitance, the dielectric material should have verylow-loss at the level of single microwave photons.

The first coupling capacitor 330 can be coupled to the first node 124 ofthe JRM 106 (through the first IDC 302) and the second couplingcapacitor 332 can be coupled to the third node 128 of the JRM 106. Infurther detail, the first lead 326 and the second lead 328 can couple totwo different sets of fingers of the first IDC 302 (illustrated at thefirst contact point 306 and a third contact point 334), that couple totwo opposite nodes of the JRM 106. This connection enables exciting thecommon mode of the JRM 106 where the two opposite nodes of the JRM 106are excited, not with opposite rf-voltage signs, but with equal signs.For example, the two opposite nodes can be excited with apositive-positive signal or a negative-negative signal.

The first lead 326 and the second lead 328 can be connectingsuperconducting wires that should be equal in length (e.g., phasematched) between the ports (e.g., the second port 320, the third port322) of the 180 degree hybrid and the coupling capacitors (e.g., thefirst coupling capacitor 330, the second coupling capacitor 332,respectively). Similarly, the first wire 132 and the second wire 134 canbe connecting superconducting wires that should be equal in length(e.g., phase matched) between the opposite nodes of the JRM 106 and theelectrodes of the first IDC 302. Also, the third wire 136 and the fourthwire 138 can be connecting superconducting wires that should be equal inlength (e.g., phase matched) between the opposite nodes of the JRM 106and the electrodes of the second capacitor 310. Further, the connectingsuperconducting wires should be as short as possible and wide (e.g.,have small series inductance).

The following provides further technical comments for an understandingof the various aspects disclosed herein. The speed of sound in thevarious piezoelectric substrates can be slower than the speed of lightby several orders of magnitude (e.g., approximately five orders ofmagnitude, for example, 10⁵).

The effective length of the superconducting SAW resonator 102 can beslightly larger than L_(a). This can be because the reflection off theBragg mirrors does not happen on the mirror edges but within a certainpenetration depth inside the Bragg mirrors.

The effective length (L_(eff)) of the superconducting SAW resonator 102and the speed of sound in the piezoelectric substrate (v_(s)) candetermine the cavity free spectral range

${({FSR})\text{:}\mspace{11mu} V_{FSR}} = {\frac{v_{s}}{2L_{eff}}.}$The SAW resonator can be similar to photonic cavities that supportmultimodes (resonances). The cavity free spectral range parameter candetermine the frequency spacing between the multimodes supported by thesuperconducting SAW resonator 102.

The larger the spacing between the Bragg mirrors, the larger L_(eff) is,and as a result the smaller the frequency separation between the SAWresonator modes. The Bragg mirrors can operate as reflective mirrorswithin a certain bandwidth. Modes that fall beyond their bandwidth arenot supported by the SAW resonator because their phononic modes are notconfined.

Depending on the V_(FSR) and the bandwidth of the Bragg mirrors, thecircuit 100 can operate over a single, a few, or many modes of the SAWresonator. It is noted that not all the modes supported by the SAWresonator would strongly couple to the JRM. Three-wave mixing operationsin the circuit 100 can take place with phononic modes that couplestrongly to the JRM. Modes couple strongly to the JRM when theiranti-nodes align with the IDC fingers coupled to the JRM.

The circuit 100 can be a three-wave mixer, such as a Josephson mixerthat relies on non-linear inductance of the Josephson junctions, whichis lossless. The Josephson mixer is used to allow mixing between phononssupported by the superconducting SAW resonator 102 and microwavesignals, which are carried by photons. This is different fromconventional devices that couple a phonon to a phonon or a photon to aphoton. Therefore, the disclosed aspects provide a significantimprovement in the coupling. For example, the circuit 100 can allowconversion from a microwave signal to acoustic waves that resonate atlow microwave frequencies. Further, the circuit 100 can amplify in anondegenerate manner Nondegenerate here means: (1) the circuit 100 isamplifying two different frequencies: one frequency at a high microwavefrequency (example 12 GHz) and another relatively low microwavefrequency (example 1 GHz), thus, nondegenerate means that thefrequencies are different so there is a spectral nondegeneracy; and (2)there is also a spatial nondegeneracy because the microwave signal issupported by the superconducting microwave resonator 104, which isphysically different than the superconducting SAW resonator 102 thatsupports the surface acoustic wave. Therefore, there is a spectral and aphysical nondegeneracy. Due to this process of parametric amplificationthat is nondegenerate, the circuit 100 can entangle a phononic mode witha photonic mode, where entanglement is a quantum property where the twomodes are strongly correlated with one another and inseparable from oneanother. Therefore, if a measurement is taken of one, the state of theother can be determined. Thus, they are entangled and they form oneentity, although they can be separated in space by distance.

FIG. 4 illustrates an example, non-limiting schematic representation ofa system 400 that comprises a unitary Josephson mixer for surfaceacoustic waves (phonons) and microwave signals (photons) in accordancewith one or more embodiments described herein. Repetitive description oflike elements employed in other embodiments described herein is omittedfor sake of brevity. The system 400 can comprise one or more of thecomponents and/or functionality of the circuit 100, and vice versa.

The system 400 can comprise a microwave Josephson mixer 402 (e.g., thecircuit 100 of FIG. 1). Mixers that are used traditionally incommunications or other microwave applications can mix togethermicrowave signals. However, traditional mixers do not mix together SAWwaves and microwave signals in a lossless manner, as discussed hereinand facilitated by the microwave Josephson mixer 402.

The microwave Josephson mixer 402 can receive, from the superconductingSAW resonator 102 (of the circuit 100) a surface acoustic wave signal(e.g., a SAW signal 404). The SAW signal 404 can comprise one or morephonons that can resonate at a first frequency. Further, the microwaveJosephson mixer 402 can receive from the superconducting microwaveresonator 104 (of the circuit 100) a microwave signal 406. The microwavesignal 406 can comprise one or more photons that can resonate at asecond frequency. For example, there can be a first port (e.g., thesignal port 212) that can support the SAW signal 404 and a second port(e.g., the idler port 216) that can support the microwave signal 406.Further, a third port (e.g., the pump port 218) can support a microwavecontrol signal 408 (also referred to a microwave drive signal).

The microwave control signal 408 can have a third frequency (f_(d)) thatis larger than the microwave signal 406, which can have a secondfrequency (f₂) that is larger than a first frequency f₁ of the SAWsignal 404. In an example, the microwave control signal 408 frequency(f_(d)) can be equal to the absolute value of the microwave signal 406frequency (f₂) minus the SAW signal 404 frequency (f₁). This can beexpressed as: f_(d)=|f₂−f₁|.

The microwave Josephson mixer 402 can operate as a lossless microwaveJosephson mixer between the SAW signal 404 that supports phonons and themicrowave control signal 408 that is carried by photons. By way ofexplanation and not limitation, as compared to standard microwaveJosephson mixer terminology, the SAW signal 404 frequency (f₁) canrelate to an Intermediate Frequency (IF), the microwave signal frequency(f₂) can relate to a Radio Frequency (RF), and the microwave controlsignal 408 (or drive signal) frequency f_(d=|)f₂−f₁|, can relate to aLocal Oscillator (LO).

Quantum information carried and/or stored by a superconducting SAWresonator 102 can be transferred to/from the superconducting microwaveresonator 104 using the microwave Josephson mixer 402 and the microwavecontrol signal 408. Accordingly, the microwave Josephson mixer 402 canmix the SAW signal 404 and the microwave signal 406 based on themicrowave control signal 408 received from a microwave source (e.g., fedthrough the pump port 218).

The microwave Josephson mixer 402 can transfer information from thesuperconducting SAW resonator 102 to the superconducting microwaveresonator 104 based on a first frequency of the microwave control signal408. In another example, the microwave Josephson mixer 402 can transferinformation from the superconducting microwave resonator 104 to thesuperconducting SAW resonator 102 based on a second frequency of themicrowave control signal 408. For example, a microwave source (e.g., atthe pump port 218) can be operated at a first frequency for a firsttransfer of first information from the superconducting SAW resonator 102to the superconducting microwave resonator 104. Further, the microwavesource can be operated at a second frequency for a second transfer ofsecond information from the superconducting microwave resonator 104 tothe superconducting SAW resonator 102.

It is noted that in FIG. 4, the signal is input on the superconductingSAW resonator 102 and output through the superconducting microwaveresonator 104. However, the device can be bidirectional and, the signalcan be input on the superconducting microwave resonator 104 and outputon the superconducting SAW resonator 102. The pump frequency is the samein both cases.

According to some implementations, the microwave Josephson mixer 402 canbe utilized as a switch that connects and/or disconnects thesuperconducting SAW resonator 102 to/from the superconducting microwaveresonator 104. The connection and/or disconnection can be based on thepresence or the absence of the microwave control signal 408. Forexample, if there is no microwave control signal 408, thesuperconducting SAW resonator 102 and the superconducting microwaveresonator 104 are not connected (e.g., there is no transfer ofinformation between the resonators). However, if there is a microwavecontrol signal 408, the microwave Josephson mixer 402 can facilitate thetransfer of information between the superconducting SAW resonator 102and the superconducting microwave resonator 104.

Further, an amplitude of the microwave control signal 408 can bemodified by the microwave source generating the microwave control signal408. The amplitude of the microwave control signal 408 can determinewhether all or part of the quantum information is transferred(transduced) between the two resonators/modes. Thus, frequency of themicrowave control signal 408 can be utilized, by the microwave Josephsonmixer 402, to select the modes whose information is swapped ortransduced. Further, the microwave Josephson mixer 402 can preserve anenergy and a coherence of the transferred quantum signal (information).

FIG. 5 illustrates an example, non-limiting schematic representation ofa system 500 that comprises a lossless frequency converter between asurface acoustic wave and a microwave signal in accordance with one ormore embodiments described herein. Repetitive description of likeelements employed in other embodiments described herein is omitted forsake of brevity. The system 500 can comprise one or more of thecomponents and/or functionality of the circuit 100, the system 400, andvice versa.

As illustrated, the system 500 can comprise the superconducting SAWresonator 102, the superconducting microwave resonator 104, and the JRM106. In this mode of operation, the amplitude of the microwave controlsignal 408 (at the pump port 218) can enable full transduction of thequantum information between the superconducting SAW resonator 102 andthe superconducting microwave resonator 104. Further to this mode ofoperation, the microwave frequency of the signal carrier can beupconverted or downconverted (depending on whether the input signal forthe device is the SAW signal 404 or a microwave reflection signal 508,respectively).

In further detail, a propagating Radio Frequency (RF) signal in therange of around 0.5 GHz to about 5 GHz can be mapped to a phononic modein the superconducting SAW resonator 102. The phononic mode can beupconverted to the superconducting microwave resonator 104 via theapplication of the microwave control signal 408, giving rise to alossless three-wave mixing interaction. The upconverted microwave signalcan become propagating upon leaving the superconducting microwaveresonator. The opposite process can also take place in the system 500 ata frequency converter 502 (e.g., the circuit 100 of FIG. 1) and asillustrated by the SAW reflection signal 506. Thus, the frequency of thesignal can be converted from f₁ to f₂, or from f₂ to f₁.

The pump signal (e.g., the microwave control signal 408) can be utilizedto facilitate the conversion. For example, the SAW signal 404 canpropagate on a transmission line 504 that can be mapped to a phonic modein the superconducting SAW resonator 102. Thus, the frequency convertercan receive, from the superconducting SAW resonator 102, the SAW signal404 that can comprise one or more phonons that resonate at a firstfrequency.

The SAW signal 404 can undergo three-wave mixing at the JRM 106. Tofacilitate the three-wave mixing, the frequency converter 502 canreceive a microwave control signal 408.

Upon or after the three-wave mixing, the JRM 106 can upconvert the SAWsignal 404 to the microwave signal 406. The upconverted signal can exitat the idler port 216 and can propagate on the transmission line 504.For example, the frequency converter 502 can implement a losslessfrequency conversion between first information of the superconductingSAW resonator 102 and second information of the superconductingmicrowave resonator 104 based on a pump signal (e.g., the microwavecontrol signal 408) received from the microwave source. The oppositeprocess operates in a similar manner.

The microwave control signal 408 frequency (f_(d)) can be equal to theabsolute value of the microwave signal 406 frequency (f₂) minus the SAWsignal 404 frequency (f₁). This can be expressed as: f_(d)=|f₂−f₁|.Therefore, a first value of the microwave control signal frequency canbe equal to an absolute value of the frequency difference between theresonance frequencies of the superconducting microwave resonator 104 andthe superconducting SAW resonator 102.

According to some aspects, implementation of the lossless frequencyconversion can comprise mapping a propagating radio frequency signal toa phononic mode in the superconducting SAW resonator 102. Further tothese aspects, the frequency converter 502 can upconvert the phononicmode to a photonic mode in the superconducting microwave resonator 104via an application of a microwave control signal frequency (e.g., themicrowave control signal 408) with a defined frequency. Up-conversion ofthe phononic mode is facilitated by a lossless three-wave mixinginteraction. Further, an upconverted microwave signal can propagate uponleaving the superconducting microwave resonator 104.

In accordance with an aspect, implementing the lossless frequencyconversion can comprise mapping a propagating radio frequency signal toa photonic mode in the superconducting microwave resonator 104. Furtherto these aspects, the frequency converter 502 can downconvert thephotonic mode to a phononic mode in the superconducting SAW resonator102 via an application of a microwave control signal 408 with a definedfrequency. The downconversion of the photonic signal can be facilitatedby the lossless three-wave mixing interaction. Further, thedownconverted surface acoustic wave signal can propagate upon leavingthe superconducting SAW resonator 102.

According to some implementations, the frequency converter 502 cantransfer information from the superconducting SAW resonator 102 to thesuperconducting microwave resonator 104 based on a frequency of themicrowave control signal 408. Additionally, or alternatively, thefrequency converter 502 can transfer information (e.g., quantuminformation) from the superconducting microwave resonator to thesuperconducting surface acoustic wave resonator based on a frequency ofthe microwave control signal.

The conversion process in the system 500 (as well as other systemsdiscussed herein) can be partial. Thus, a first set of information canbe converted, while a second set of the information can be retained andreflected back to the respective incoming port. Further, some of theinformation can be converted using a switch (e.g., implemented by theJRM 106 and the presence and/or absence of the microwave control signal408) where the frequency determines which SAW mode is coupled to themicrowave signal as a selector and/or as a switch. In the case of aswitch if there is no pump signal, there is no conversion.

FIG. 6 illustrates an example, non-limiting schematic representation ofa system 600 that comprises a nondegenerate parametric Josephsonamplifier for surface acoustic waves and microwave signals in accordancewith one or more embodiments described herein. Repetitive description oflike elements employed in other embodiments described herein is omittedfor sake of brevity. The system 600 can comprise one or more of thecomponents and/or functionality of the circuit 100, the system 400, thesystem 500, and vice versa.

The system 600 can comprise a Josephson parametric amplifier 602 thatcan function as a phase-preserving quantum-limited amplifier forlow-frequency and high-frequency microwave signals. The two quadraturesof incoming microwave-signals entering the two ports (e.g., the signalport 212 and the idler port 216) can be amplified at the quantum limit.Amplified outgoing signals can comprise an amplified SAW signal 604 and,an amplified microwave signal 606. The amplified outgoing signals cancomprise same-frequency signals reflecting off the same port andfrequency-converted signals transmitted to the other port. The incomingsignals are represented as small arrows (e.g., weak signals) and theoutgoing signals are represented as larger arrows to indicateamplification. Microwave signals, and other parametric signals, can bedefined by two quadratures, namely, the amplitude of the signal and thephase of the signal.

In further detail, propagating radio frequency and microwave signals canbe mapped respectively to at least one of the phononic modes of thesuperconducting SAW resonator 102 and at least one of the microwavemodes in the superconducting microwave resonator 104. According to someimplementations, the phononic modes and the microwave modes can be thefundamental modes, however, the disclosed aspects are not limited to thefundamental modes and other modes can be utilized. The phononic modesand the microwave modes can be amplified at the quantum limit via theapplication of the microwave drive signal giving rise to a losslessthree-wave mixing interaction and mapped back to reflected (e.g., samefrequency) and transmitted (e.g., different frequency) amplified radiofrequency/microwave signals.

The amplification of the system 700 is nondegenerate. Thus, the twomodes can have two different frequencies and can have two differentports. The amplification created by the system 600 can preserve thephase of the microwave signal. Thus, the system 600 can amplify bothquadratures of the microwave field, by the same, or a similar, amount.For example, if one quadrature is amplified by a factor of 100, theother quadrature is also amplified by a factor of 100.

According to some implementations, the Josephson parametric amplifier602 can amplify first quadratures of the SAW signal 404 entering a firstport (e.g., the signal port 212) and second quadratures of a microwavesignal 406 entering a second port (e.g., the idler port 216). The firstquadratures can comprise a first amplitude and a first phase and thesecond quadratures can comprise a second amplitude and a second phase.Further, a first amplified signal can be output through an output port.The first amplified signal comprises a first reflective signal and afirst transmitted signal and a second amplified signal that comprises asecond reflective signal and a second transmitted signal. Theamplification can include amplification of the first quadratures of thesurface acoustic wave signal and the second quadratures of the microwavesignal at a defined amplitude gain.

For example, the first reflective signal can comprise a firstsame-frequency signal reflecting off the first port and the firsttransmitted signal can comprise a first frequency-converted signaltransmitted to the second port. Further, the second reflective signalcan comprise a second same-frequency signal reflecting off the secondport and the second transmitted signal can comprise a secondfrequency-converted signal transmitted to the first port.

FIG. 7 illustrates an example, non-limiting schematic representation ofa system 700 that comprises an entangler of a phononic mode and aphotonic mode in accordance with one or more embodiments describedherein. Repetitive description of like elements employed in otherembodiments described herein is omitted for sake of brevity. The system700 can comprise one or more of the components and/or functionality ofthe circuit 100, the system 400, the system 500, the system 600, andvice versa.

The system 700 can comprise an entanglement component 702 that cangenerate entanglement between a phononic mode and a photonic mode. Thesystem 700 can also comprise a first superconducting qubit 704capacitively coupled to the superconducting SAW resonator 102 and asecond superconducting qubit 706 capacitively coupled to thesuperconducting microwave resonator 104. Further, the JRM 106 can becoupled to the superconducting SAW resonator 102 and the superconductingmicrowave resonator 104. Also included in the system 700 can be a pumpdrive (e.g., fed through the pump port 218) operatively coupled to twoadjacent nodes of the JRM 106 via the first coupling capacitor 330 andvia the second coupling capacitor 332.

According to an implementation, the pump port 218 can input an inputsignal, that comprises a first frequency, into the JRM 106. The firstsuperconducting qubit 704 can be operatively coupled to the entanglementcomponent 702 via the superconducting SAW resonator 102 and the secondsuperconducting qubit 706 can be operatively coupled to the entanglementcomponent 702 via the superconducting microwave resonator 104. Further,the entanglement component 702 can output an output signal thatcomprises an entangled signal that comprises a second frequency of thesuperconducting SAW resonator 102 and a third frequency of thesuperconducting microwave resonator 104. According to someimplementations, the entanglement component 702 can generate theentangled signal between one or more phonons of a surface acoustic wave(e.g., the amplified SAW signal 604) output by the superconducting SAWresonator 102 and one or more microwave photons (e.g., the amplifiedmicrowave signal 606) output by the superconducting microwave resonator104.

When the entanglement component 702 is operated as a nondegenerateamplifier, entanglement can be generated between the phonons of a SAWsignal supported by the superconducting SAW resonator 102 and themicrowave photons supported by the superconducting microwave resonator104. For example, the entanglement can be utilized to entanglesuperconducting qubits capacitively coupled to the entanglementcomponent 702. It is noted that in practice, the qubits are not directlycoupled to the entanglement component 702. Instead, the qubits arecoupled to microwave readout resonators which are, in turn, coupled tothe entanglement component 702.

According to some implementations, the parametric amplification cancreate entanglement. Entanglement can occur when the reflected signal isnot purely the incoming signal amplified, but is an entangled version ofthe input signals. For example, the entangled signal can comprise someinformation coming from the other port. It is noted that the signal isnot simply reflected with gain or reflected with amplification. Sincethere is a three-wave mixing occurring, a portion of the signal isreflected, and another portion is also converted in frequency andtransmitted to the other port. For example, the output microwave signalis not purely the input microwave signal amplified, but has also aportion of the SAW signal that was amplified and upconverted infrequency. Thus, the output microwave signal can be a mixture of areflected incoming microwave signal through the idler port 216 and afrequency-converted transmitted SAW signal entering through the signalport 212. Therefore, the output microwave signal can carry informationcomprising portions of the two input signals.

As illustrated, there can be one or more qubits, illustrated as thefirst superconducting qubit 704 and the second superconducting qubit706, coupled to the entanglement component 702. It is noted that, forpurposes of simplification, protection elements (e.g., components thatprotect the qubits from the amplified signal) between the firstsuperconducting qubit 704 and the entanglement component 702, andbetween the second superconducting qubit 706 and the entanglementcomponent 702 are not illustrated (such as microwave circulators andisolators). The pump frequency f_(d) is the sum of the two frequencies.Therefore, the information of the first superconducting qubit 704 can beentangled with the information of the second superconducting qubit 706.Thus, the first superconducting qubit 704 and the second superconductingqubit 706 can be effectively entangled together.

For example, a first measurement can be performed on the firstsuperconducting qubit 704 and a second measurement can be performed onthe second superconducting qubit 706. The first measurement and thesecond measurement enter the entanglement component 702 and areamplified at the output. Therefore, a joint measurement of the firstmeasurement and the second measurement can be performed. The jointmeasurement creates entanglement between the first superconducting qubit704 and the second superconducting qubit 706. In this configuration, thefirst superconducting qubit 704 could be strongly coupled to multimodes,while the second superconducting qubit 706 can be coupled to a singlemode.

FIG. 8 illustrates a flow diagram of an example, non-limiting, method800 for mixing surface acoustic waves (phonons) and microwave signals(photons) in accordance with one or more embodiments described herein.Repetitive description of like elements employed in other embodimentsdescribed herein is omitted for sake of brevity.

At 802 of the method 800, a surface acoustic wave signal (e.g., the SAWsignal 404) that comprise one or more phonons that can resonate at a lowfrequency can be received (e.g., via the microwave Josephson mixer 402).The surface acoustic wave signal can be received from a superconductingsurface acoustic wave resonator (e.g., the superconducting SAW resonator102) of a device (e.g., the circuit 100). For example, external signalscoming from quantum systems enter the device ports and can be mapped tophononic and photonic modes in the microwave resonator and the SAWresonator.

Further, at 804 of the method 800, a microwave signal (e.g., themicrowave signal 406) that comprises one or more photons that canresonate at a second frequency can be received (e.g., via the microwaveJosephson mixer 402). The microwave signal can be received from asuperconducting microwave resonator (e.g., the superconducting microwaveresonator 104).

At 806 of the method 800, the surface acoustic wave signal and themicrowave signal can be mixed (e.g., via the microwave Josephson mixer402). The mixing can be based on a microwave control signal (e.g., themicrowave control signal 408) received from a microwave source (e.g.,fed through the pump port 218). According to some implementations,mixing the surface acoustic wave signal and the microwave signal cancomprise preserving, by the microwave Josephson mixer and the microwavecontrol signal, the quantum information carried by the surface acousticwave signal and/or the microwave signal. Thus, external signals comingfrom quantum systems enter the device ports and are mapped to phononicand photonic modes in the microwave resonator and the SAW resonator.

The method 800 can perform dissipationless, three-wave mixing andamplification between low microwave frequencies of the superconductingsurface acoustic wave resonator and high microwave frequencies of thesuperconducting microwave resonator. Further, quantum informationcarried by a surface acoustic wave signal can be transduced into amicrowave signal or vice versa in a unitary manner (e.g., the energy andphase coherence of the quantum signal are preserved). Also, this quantumoperation can be controlled and enabled by a separate microwave controlsignal (referred to as the pump) received by the device.

FIG. 9 illustrates a flow diagram of an example, non-limiting, method900 for mixing surface acoustic waves and microwave signals based on afrequency of a microwave control signal in accordance with one or moreembodiments described herein. Repetitive description of like elementsemployed in other embodiments described herein is omitted for sake ofbrevity.

At 902 of the method 900, a surface acoustic wave signal (e.g., the SAWsignal 404) and a microwave signal (e.g., the microwave signal 406) canbe mixed (e.g., via the microwave Josephson mixer 402). For example, themixing by the microwave Josephson mixer can be based on a microwavecontrol signal (e.g., the microwave control signal 408) received from amicrowave source (e.g., fed through the pump port 218) operativelycoupled to the microwave Josephson mixer.

The pump drive can be applied at the frequency difference between themicrowave and SAW signals. For example, at 904 of the method 900, afirst quantum information can be transferred from the superconductingsurface acoustic wave resonator (e.g., the superconducting SAW resonator102) to the superconducting microwave resonator (e.g., thesuperconducting microwave resonator 104) and second quantum informationcan be transferred from the superconducting microwave resonator to thesuperconducting surface acoustic wave resonator. The transfer of thefirst quantum information and the second information can be enabled by amicrowave control signal received by the microwave Josephson mixer.Thus, the same pump frequency and amplitude can be applied fortransducing a same amount of information in both directions (e.g., fromthe superconducting surface acoustic wave to the superconductingmicrowave resonator and from the superconducting microwave resonator tothe superconducting surface acoustic wave).

FIG. 10 illustrates a flow diagram of an example, non-limiting, method1000 for operations of a switch utilized to mix surface acoustic wavesand microwave signals based on a frequency and amplitude of a microwavecontrol signal in accordance with one or more embodiments describedherein. Repetitive description of like elements employed in otherembodiments described herein is omitted for sake of brevity.

At 1002 of the method 1000, a connection between the superconductingsurface acoustic wave resonator and the superconducting microwaveresonator can be disconnected (e.g., via the microwave Josephson mixer402 or the JRM 106). The disconnection can be based on a firstdetermination that the mixing of the surface acoustic wave signal andthe microwave signal is to be stopped. Thus, communication between thesuperconducting surface acoustic wave resonator and the superconductingmicrowave resonator is disconnected.

Further, at 1004 of the method 1000, the connection between thesuperconducting surface acoustic wave resonator and the superconductingmicrowave resonator can be reenabled (e.g., via the microwave Josephsonmixer 402 or the JRM 106). Reenabling the connection can be based on asecond determination that the mixing of the surface acoustic wave signaland the microwave signal is to be restarted. Thus, communication betweenthe superconducting surface acoustic wave resonator and thesuperconducting microwave resonator is enabled (or connected).

FIG. 11 illustrates a flow diagram of an example, non-limiting, method1100 for mixing surface acoustic waves and microwave signals based on anamplitude of a microwave signal in accordance with one or moreembodiments described herein. Repetitive description of like elementsemployed in other embodiments described herein is omitted for sake ofbrevity.

At 1102 of the method 1100, a surface acoustic wave signal (e.g., theSAW signal 404) and a microwave signal (e.g., the microwave signal 406)can be received (e.g., via the microwave Josephson mixer 402). At 1104of the method 1100, the surface acoustic wave signal and the microwavesignal can be mixed (e.g., via the microwave Josephson mixer 402). Themixing can be based on a microwave control signal (e.g., the microwavecontrol signal 408) received from a microwave source (e.g., fed throughthe pump port 218).

Further, at 1106 of the method 1100, a first portion of quantuminformation can be transferred between the superconducting surfaceacoustic wave resonator and the superconducting microwave resonatorbased on a first amplitude of the microwave control signal (e.g., viathe microwave Josephson mixer 402). At 1108 of the method 1100, a secondportion of quantum information can be transferred between thesuperconducting surface acoustic wave resonator and the superconductingmicrowave resonator based on a second amplitude of the microwave controlsignal (e.g., via the microwave Josephson mixer 402). For example, afirst amplitude can be utilized to transfer a first portion ofinformation between the superconducting surface acoustic wave resonatorand the superconducting microwave resonator. A second amplitude can beutilized to transfer a second portion of the information between thesuperconducting surface acoustic wave resonator and the superconductingmicrowave resonator.

FIG. 12 illustrates a flow diagram of an example, non-limiting, method1200 for a lossless frequency conversion between a surface acoustic waveand a microwave signal in accordance with one or more embodimentsdescribed herein. Repetitive description of like elements employed inother embodiments described herein is omitted for sake of brevity.

At 1202 of the method 1200, a surface acoustic wave signal (e.g., theSAW signal 404) can be received (e.g., via the frequency converter 502).Further, at 1204 of the method 1200 a microwave signal (e.g., themicrowave signal 406) can be received (e.g., via the frequency converter502). At 1206 of the method 1200, a lossless frequency conversion can beimplemented between first information of the superconducting surfaceacoustic wave resonator and second information of the superconductingmicrowave resonator based on a pump signal received from a microwavesource (e.g., via the frequency converter 502).

According to some implementations, the frequency converter can transferquantum information from the superconducting surface acoustic waveresonator to the superconducting microwave resonator based on thefrequency and amplitude of the microwave control signal and vice versa.

FIG. 13 illustrates a flow diagram of an example, non-limiting, method1300 for performing an up-conversion between a surface acoustic wavesignal and a microwave signal in accordance with one or more embodimentsdescribed herein. Repetitive description of like elements employed inother embodiments described herein is omitted for sake of brevity.

At 1302, a propagating radio frequency signal can be mapped to aphononic mode in a superconducting surface acoustic wave resonator(e.g., via the frequency converter 502). Further, at 1304, the phononicmode can be upconverted to a photonic mode in the superconductingmicrowave resonator via an application of a microwave control signal(e.g., via the frequency converter 502) of a microwave source.Upconverting the photonic mode is enabled by a lossless three-wavemixing interaction. An upconverted microwave signal can propagate uponleaving the superconducting microwave resonator. According to someimplementations, the microwave control signal frequency can be equal toan absolute value of the resonance frequency of the superconductingmicrowave resonator minus the resonance frequency of the SAW resonator.

FIG. 14 illustrates a flow diagram of an example, non-limiting, method1400 for performing a down-conversion between a surface acoustic wavesignal and a microwave signal in accordance with one or more embodimentsdescribed herein. Repetitive description of like elements employed inother embodiments described herein is omitted for sake of brevity.

At 1402 of the method 1400, a propagating microwave frequency signal canbe mapped to a photonic mode in the superconducting microwave resonator(e.g., via the frequency converter 502). At 1404 of the method 1400, thephotonic mode can be downconverted to a phononic mode in thesuperconducting surface acoustic wave resonator via an application of amicrowave control signal (e.g., via the frequency converter 502) of amicrowave source. Downconverting the photonic mode is enabled by alossless three-wave mixing interaction. Further, a downconverted surfaceacoustic wave signal propagates upon leaving the superconducting SAWresonator.

FIG. 15 illustrates a flow diagram of an example, non-limiting, method1500 for performing nondegenerate parametric amplification for surfaceacoustic waves and microwave signals in accordance with one or moreembodiments described herein. Repetitive description of like elementsemployed in other embodiments described herein is omitted for sake ofbrevity.

At 1502 of the method 1500, first quadratures of a surface acoustic wavesignal entering a first port of a device and second quadratures of amicrowave signal entering a second port of the device can be amplified(e.g., via the Josephson parametric amplifier 602). In an example, theamplification can comprise amplifying the first quadratures of thesurface acoustic wave signal and the second quadratures of the microwavesignal at a defined amplitude gain value (e.g., measured with respect tonoise or a reference when no microwave control signal is applied to thesuperconducting device).

Further, at 1504, the method 1500 can output, through a first outputport, a first amplified signal that comprises a first output signal anda first transmitted signal with frequency conversion and, through asecond output port, a second amplified signal that comprises a secondoutput signal and a second transmitted signal with the frequencyconversion (e.g., Josephson parametric amplifier 602). According to someimplementations, the first output signal can comprise a firstsame-frequency signal reflecting off the first port and a firsttransmitted signal can comprise a first frequency-converted signaltransmitted from the second port to the first port. Further, the secondoutput signal can comprise a second same-frequency signal reflecting offthe second port and a second transmitted signal can comprise a secondfrequency-converted signal transmitted from the first port to the secondport.

FIG. 16 illustrates a flow diagram of an example, non-limiting, method1600 for entangling a phononic mode and a photonic mode of a quantumcircuit in accordance with one or more embodiments described herein.Repetitive description of like elements employed in other embodimentsdescribed herein is omitted for sake of brevity.

At 1602, a first input signal that comprises a first frequency can beinput into a superconducting surface acoustic wave resonator (e.g., viathe entanglement component 702). At 1604, a second input signal thatcomprises a second frequency can be input into a superconductingmicrowave resonator.

Further, at 1606 of the method 1600 an output signal that comprises anentangled signal that comprises an amplified superposition of the inputfields (or input signals) entering the superconducting microwave and SAWresonators can be output (e.g., via the entanglement component 702). Forexample, the input filed (or input signals) can be the first inputsignal and the second input signal. The method can include generatingthe entangled signal between one or more phonons of a surface acousticwave output by the superconducting surface acoustic wave resonator andone or more microwave photons output by the superconducting microwaveresonator.

A first qubit can be operatively coupled to the entanglement componentvia the superconducting surface acoustic wave resonator. Further, asecond qubit can be operatively coupled to the entanglement componentvia the superconducting microwave resonator. In some implementations,the first qubit can be operatively coupled to two or more modes.Further, to these implementations the second qubit can be operativelycoupled to a single mode. The entangled signal can comprise anentanglement between a phononic mode and a photonic mode. According tosome implementations, the entangled signal can comprise an amplifiedsuperposition of input signals entering the superconducting microwaveresonator and the superconducting surface acoustic wave resonator.

For simplicity of explanation, the methodologies are depicted anddescribed as a series of acts. It is to be understood and appreciatedthat the subject innovation is not limited by the acts illustratedand/or by the order of acts, for example acts can occur in variousorders and/or concurrently, and with other acts not presented anddescribed herein. Furthermore, not all illustrated acts can be requiredto implement the methodologies in accordance with the disclosed subjectmatter. In addition, those skilled in the art will understand andappreciate that the methodologies could alternatively be represented asa series of interrelated states via a state diagram or events.Additionally, it should be further appreciated that the methodologiesdisclosed hereinafter and throughout this specification are capable ofbeing stored on an article of manufacture to facilitate transporting andtransferring such methodologies to computers. The term article ofmanufacture, as used herein, is intended to encompass a computer programaccessible from any computer-readable device or storage media.

In order to provide a context for the various aspects of the disclosedsubject matter, FIG. 17 as well as the following discussion are intendedto provide a general description of a suitable environment in which thevarious aspects of the disclosed subject matter can be implemented. FIG.17 illustrates a block diagram of an example, non-limiting operatingenvironment in which one or more embodiments described herein can befacilitated. Repetitive description of like elements employed in otherembodiments described herein is omitted for sake of brevity. Withreference to FIG. 17, a suitable operating environment 1700 forimplementing various aspects of this disclosure can also include acomputer 1712. The computer 1712 can also include a processing unit1714, a system memory 1716, and a system bus 1718. The system bus 1718couples system components including, but not limited to, the systemmemory 1716 to the processing unit 1714. The processing unit 1714 can beany of various available processors. Dual microprocessors and othermultiprocessor architectures also can be employed as the processing unit1714. The system bus 1718 can be any of several types of busstructure(s) including the memory bus or memory controller, a peripheralbus or external bus, and/or a local bus using any variety of availablebus architectures including, but not limited to, Industrial StandardArchitecture (ISA), Micro-Channel Architecture (MSA), Extended ISA(EISA), Intelligent Drive Electronics (IDE), VESA Local Bus (VLB),Peripheral Component Interconnect (PCI), Card Bus, Universal Serial Bus(USB), Advanced Graphics Port (AGP), Firewire (IEEE 1394), and SmallComputer Systems Interface (SCSI). The system memory 1716 can alsoinclude volatile memory 1720 and nonvolatile memory 1722. The basicinput/output system (BIOS), containing the basic routines to transferinformation between elements within the computer 1712, such as duringstart-up, is stored in nonvolatile memory 1722. By way of illustration,and not limitation, nonvolatile memory 1722 can include read only memory(ROM), programmable ROM (PROM), electrically programmable ROM (EPROM),electrically erasable programmable ROM (EEPROM), flash memory, ornonvolatile random access memory (RAM) (e.g., ferroelectric RAM(FeRAM)). Volatile memory 1720 can also include random access memory(RAM), which acts as external cache memory. By way of illustration andnot limitation, RAM is available in many forms such as static RAM(SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rateSDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM),direct Rambus RAM (DRRAM), direct Rambus dynamic RAM (DRDRAM), andRambus dynamic RAM.

Computer 1712 can also include removable/non-removable,volatile/nonvolatile computer storage media. FIG. 17 illustrates, forexample, a disk storage 1724. Disk storage 1724 can also include, but isnot limited to, devices like a magnetic disk drive, floppy disk drive,tape drive, Jaz drive, Zip drive, LS-100 drive, flash memory card, ormemory stick. The disk storage 1724 also can include storage mediaseparately or in combination with other storage media including, but notlimited to, an optical disk drive such as a compact disk ROM device(CD-ROM), CD recordable drive (CD-R Drive), CD rewritable drive (CD-RWDrive) or a digital versatile disk ROM drive (DVD-ROM). To facilitateconnection of the disk storage 1724 to the system bus 1718, a removableor non-removable interface is typically used, such as interface 1726.FIG. 17 also depicts software that acts as an intermediary between usersand the basic computer resources described in the suitable operatingenvironment 1700. Such software can also include, for example, anoperating system 1728. Operating system 1728, which can be stored ondisk storage 1724, acts to control and allocate resources of thecomputer 1712. System applications 1730 take advantage of the managementof resources by operating system 1728 through program modules 1732 andprogram data 1734, e.g., stored either in system memory 1716 or on diskstorage 1724. It is to be appreciated that this disclosure can beimplemented with various operating systems or combinations of operatingsystems. A user enters commands or information into the computer 1712through input device(s) 1736. Input devices 1736 include, but are notlimited to, a pointing device such as a mouse, trackball, stylus, touchpad, keyboard, microphone, joystick, game pad, satellite dish, scanner,TV tuner card, digital camera, digital video camera, web camera, and thelike. These and other input devices connect to the processing unit 1714through the system bus 1718 via interface port(s) 1738. Interfaceport(s) 1738 include, for example, a serial port, a parallel port, agame port, and a universal serial bus (USB). Output device(s) 1740 usesome of the same type of ports as input device(s) 1736. Thus, forexample, a USB port can be used to provide input to computer 1712, andto output information from computer 1712 to an output device 1740.Output adapter 1742 is provided to illustrate that there are some outputdevices 1740 like monitors, speakers, and printers, among other outputdevices 1740, which require special adapters. The output adapters 1742include, by way of illustration and not limitation, video and soundcards that provide a method of connection between the output device 1740and the system bus 1718. It should be noted that other devices and/orsystems of devices provide both input and output capabilities such asremote computer(s) 1744.

Computer 1712 can operate in a networked environment using logicalconnections to one or more remote computers, such as remote computer(s)1744. The remote computer(s) 1744 can be a computer, a server, a router,a network PC, a workstation, a microprocessor based appliance, a peerdevice or other common network node and the like, and typically can alsoinclude many or all of the elements described relative to computer 1712.For purposes of brevity, only a memory storage device 1746 isillustrated with remote computer(s) 1744. Remote computer(s) 1744 islogically connected to computer 1712 through a network interface 1748and then physically connected via communication connection 1750. Networkinterface 1748 encompasses wire and/or wireless communication networkssuch as local-area networks (LAN), wide-area networks (WAN), cellularnetworks, etc. LAN technologies include Fiber Distributed Data Interface(FDDI), Copper Distributed Data Interface (CDDI), Ethernet, Token Ringand the like. WAN technologies include, but are not limited to,point-to-point links, circuit switching networks like IntegratedServices Digital Networks (ISDN) and variations thereon, packetswitching networks, and Digital Subscriber Lines (DSL). Communicationconnection(s) 1750 refers to the hardware/software employed to connectthe network interface 1748 to the system bus 1718. While communicationconnection 1750 is shown for illustrative clarity inside computer 1712,it can also be external to computer 1712. The hardware/software forconnection to the network interface 1748 can also include, for exemplarypurposes only, internal and external technologies such as, modemsincluding regular telephone grade modems, cable modems and DSL modems,ISDN adapters, and Ethernet cards.

The present invention may be a system, a method, an apparatus and/or acomputer program product at any possible technical detail level ofintegration. The computer program product can include a computerreadable storage medium (or media) having computer readable programinstructions thereon for causing a processor to carry out aspects of thepresent invention. The computer readable storage medium can be atangible device that can retain and store instructions for use by aninstruction execution device. The computer readable storage medium canbe, for example, but is not limited to, an electronic storage device, amagnetic storage device, an optical storage device, an electromagneticstorage device, a semiconductor storage device, or any suitablecombination of the foregoing. A non-exhaustive list of more specificexamples of the computer readable storage medium can also include thefollowing: a portable computer diskette, a hard disk, a random accessmemory (RAM), a read-only memory (ROM), an erasable programmableread-only memory (EPROM or Flash memory), a static random access memory(SRAM), a portable compact disc read-only memory (CD-ROM), a digitalversatile disk (DVD), a memory stick, a floppy disk, a mechanicallyencoded device such as punch-cards or raised structures in a groovehaving instructions recorded thereon, and any suitable combination ofthe foregoing. A computer readable storage medium, as used herein, isnot to be construed as being transitory signals per se, such as radiowaves or other freely propagating electromagnetic waves, electromagneticwaves propagating through a waveguide or other transmission media (e.g.,light pulses passing through a fiber-optic cable), or electrical signalstransmitted through a wire.

Computer readable program instructions described herein can bedownloaded to respective computing/processing devices from a computerreadable storage medium or to an external computer or external storagedevice via a network, for example, the Internet, a local area network, awide area network and/or a wireless network. The network can comprisecopper transmission cables, optical transmission fibers, wirelesstransmission, routers, firewalls, switches, gateway computers and/oredge servers. A network adapter card or network interface in eachcomputing/processing device receives computer readable programinstructions from the network and forwards the computer readable programinstructions for storage in a computer readable storage medium withinthe respective computing/processing device. Computer readable programinstructions for carrying out operations of the present invention can beassembler instructions, instruction-set-architecture (ISA) instructions,machine instructions, machine dependent instructions, microcode,firmware instructions, state-setting data, configuration data forintegrated circuitry, or either source code or object code written inany combination of one or more programming languages, including anobject oriented programming language such as Smalltalk, C++, or thelike, and procedural programming languages, such as the “C” programminglanguage or similar programming languages. The computer readable programinstructions can execute entirely on the user's computer, partly on theuser's computer, as a stand-alone software package, partly on the user'scomputer and partly on a remote computer or entirely on the remotecomputer or server. In the latter scenario, the remote computer can beconnected to the user's computer through any type of network, includinga local area network (LAN) or a wide area network (WAN), or theconnection can be made to an external computer (for example, through theInternet using an Internet Service Provider). In some embodiments,electronic circuitry including, for example, programmable logiccircuitry, field-programmable gate arrays (FPGA), or programmable logicarrays (PLA) can execute the computer readable program instructions byutilizing state information of the computer readable programinstructions to personalize the electronic circuitry, in order toperform aspects of the present invention.

Aspects of the present invention are described herein with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems), and computer program products according to embodiments of theinvention. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer readable program instructions. These computer readable programinstructions can be provided to a processor of a general purposecomputer, special purpose computer, or other programmable dataprocessing apparatus to produce a machine, such that the instructions,which execute via the processor of the computer or other programmabledata processing apparatus, create method for implementing thefunctions/acts specified in the flowchart and/or block diagram block orblocks. These computer readable program instructions can also be storedin a computer readable storage medium that can direct a computer, aprogrammable data processing apparatus, and/or other devices to functionin a particular manner, such that the computer readable storage mediumhaving instructions stored therein comprises an article of manufactureincluding instructions which implement aspects of the function/actspecified in the flowchart and/or block diagram block or blocks. Thecomputer readable program instructions can also be loaded onto acomputer, other programmable data processing apparatus, or other deviceto cause a series of operational acts to be performed on the computer,other programmable apparatus or other device to produce a computerimplemented process, such that the instructions which execute on thecomputer, other programmable apparatus, or other device implement thefunctions/acts specified in the flowchart and/or block diagram block orblocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods, and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams can represent a module, segment, or portionof instructions, which comprises one or more executable instructions forimplementing the specified logical function(s). In some alternativeimplementations, the functions noted in the blocks can occur out of theorder noted in the Figures. For example, two blocks shown in successioncan, in fact, be executed substantially concurrently, or the blocks cansometimes be executed in the reverse order, depending upon thefunctionality involved. It will also be noted that each block of theblock diagrams and/or flowchart illustration, and combinations of blocksin the block diagrams and/or flowchart illustration, can be implementedby special purpose hardware-based systems that perform the specifiedfunctions or acts or carry out combinations of special purpose hardwareand computer instructions.

While the subject matter has been described above in the general contextof computer-executable instructions of a computer program product thatruns on a computer and/or computers, those skilled in the art willrecognize that this disclosure also can be implemented in combinationwith other program modules. Generally, program modules include routines,programs, components, data structures, etc. that perform particulartasks and/or implement particular abstract data types. Moreover, thoseskilled in the art will appreciate that the inventivecomputer-implemented methods can be practiced with other computer systemconfigurations, including single-processor or multiprocessor computersystems, mini-computing devices, mainframe computers, as well ascomputers, hand-held computing devices (e.g., PDA, phone),microprocessor-based or programmable consumer or industrial electronics,and the like. The illustrated aspects can also be practiced indistributed computing environments where tasks are performed by remoteprocessing devices that are linked through a communications network.However, some, if not all aspects of this disclosure can be practiced onstand-alone computers. In a distributed computing environment, programmodules can be located in both local and remote memory storage devices.

As used in this application, the terms “component,” “system,”“platform,” “interface,” and the like, can refer to and/or can include acomputer-related entity or an entity related to an operational machinewith one or more specific functionalities. The entities disclosed hereincan be either hardware, a combination of hardware and software,software, or software in execution. For example, a component can be, butis not limited to being, a process running on a processor, a processor,an object, an executable, a thread of execution, a program, and/or acomputer. By way of illustration, both an application running on aserver and the server can be a component. One or more components canreside within a process and/or thread of execution and a component canbe localized on one computer and/or distributed between two or morecomputers. In another example, respective components can execute fromvarious computer readable media having various data structures storedthereon. The components can communicate via local and/or remoteprocesses such as in accordance with a signal having one or more datapackets (e.g., data from one component interacting with anothercomponent in a local system, distributed system, and/or across a networksuch as the Internet with other systems via the signal). As anotherexample, a component can be an apparatus with specific functionalityprovided by mechanical parts operated by electric or electroniccircuitry, which is operated by a software or firmware applicationexecuted by a processor. In such a case, the processor can be internalor external to the apparatus and can execute at least a part of thesoftware or firmware application. As yet another example, a componentcan be an apparatus that provides specific functionality throughelectronic components without mechanical parts, wherein the electroniccomponents can include a processor or other method to execute softwareor firmware that confers at least in part the functionality of theelectronic components. In an aspect, a component can emulate anelectronic component via a virtual machine, e.g., within a cloudcomputing system.

In addition, the term “or” is intended to mean an inclusive “or” ratherthan an exclusive “or.” That is, unless specified otherwise, or clearfrom context, “X employs A or B” is intended to mean any of the naturalinclusive permutations. That is, if X employs A; X employs B; or Xemploys both A and B, then “X employs A or B” is satisfied under any ofthe foregoing instances. Moreover, articles “a” and “an” as used in thesubject specification and annexed drawings should generally be construedto mean “one or more” unless specified otherwise or clear from contextto be directed to a singular form. As used herein, the terms “example”and/or “exemplary” are utilized to mean serving as an example, instance,or illustration. For the avoidance of doubt, the subject matterdisclosed herein is not limited by such examples. In addition, anyaspect or design described herein as an “example” and/or “exemplary” isnot necessarily to be construed as preferred or advantageous over otheraspects or designs, nor is it meant to preclude equivalent exemplarystructures and techniques known to those of ordinary skill in the art.

As it is employed in the subject specification, the term “processor” canrefer to substantially any computing processing unit or devicecomprising, but not limited to, single-core processors;single-processors with software multithread execution capability;multi-core processors; multi-core processors with software multithreadexecution capability; multi-core processors with hardware multithreadtechnology; parallel platforms; and parallel platforms with distributedshared memory. Additionally, a processor can refer to an integratedcircuit, an application specific integrated circuit (ASIC), a digitalsignal processor (DSP), a field programmable gate array (FPGA), aprogrammable logic controller (PLC), a complex programmable logic device(CPLD), a discrete gate or transistor logic, discrete hardwarecomponents, or any combination thereof designed to perform the functionsdescribed herein. Further, processors can exploit nano-scalearchitectures such as, but not limited to, molecular and quantum-dotbased transistors, switches and gates, in order to optimize space usageor enhance performance of user equipment. A processor can also beimplemented as a combination of computing processing units. In thisdisclosure, terms such as “store,” “storage,” “data store,” datastorage,” “database,” and substantially any other information storagecomponent relevant to operation and functionality of a component areutilized to refer to “memory components,” entities embodied in a“memory,” or components comprising a memory. It is to be appreciatedthat memory and/or memory components described herein can be eithervolatile memory or nonvolatile memory, or can include both volatile andnonvolatile memory. By way of illustration, and not limitation,nonvolatile memory can include read only memory (ROM), programmable ROM(PROM), electrically programmable ROM (EPROM), electrically erasable ROM(EEPROM), flash memory, or nonvolatile random access memory (RAM) (e.g.,ferroelectric RAM (FeRAM). Volatile memory can include RAM, which canact as external cache memory, for example. By way of illustration andnot limitation, RAM is available in many forms such as synchronous RAM(SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rateSDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM),direct Rambus RAM (DRRAM), direct Rambus dynamic RAM (DRDRAM), andRambus dynamic RAM (RDRAM). Additionally, the disclosed memorycomponents of systems or computer-implemented methods herein areintended to include, without being limited to including, these and anyother suitable types of memory.

What has been described above include mere examples of systems andcomputer-implemented methods. It is, of course, not possible to describeevery conceivable combination of components or computer-implementedmethods for purposes of describing this disclosure, but one of ordinaryskill in the art can recognize that many further combinations andpermutations of this disclosure are possible. Furthermore, to the extentthat the terms “includes,” “has,” “possesses,” and the like are used inthe detailed description, claims, appendices and drawings such terms areintended to be inclusive in a manner similar to the term “comprising” as“comprising” is interpreted when employed as a transitional word in aclaim. The descriptions of the various embodiments have been presentedfor purposes of illustration, but are not intended to be exhaustive orlimited to the embodiments disclosed. Many modifications and variationswill be apparent to those of ordinary skill in the art without departingfrom the scope and spirit of the described embodiments. The terminologyused herein was chosen to best explain the principles of theembodiments, the practical application or technical improvement overtechnologies found in the marketplace, or to enable others of ordinaryskill in the art to understand the embodiments disclosed herein.

What is claimed is:
 1. A method, comprising: mixing, by a microwaveJosephson mixer, a surface acoustic wave signal and a microwave signalbased on a microwave control signal, wherein the surface acoustic wavesignal is associated with a superconducting surface acoustic waveresonator of a superconducting device and wherein the microwave signalis associated with a superconducting microwave resonator of thesuperconducting device.
 2. The method of claim 1, further comprising:transferring, by the microwave Josephson mixer, quantum information fromthe superconducting surface acoustic wave resonator to thesuperconducting microwave resonator based on an application of pumpdrive applied at a frequency difference between a second frequency atwhich one or more photons of the microwave signal resonate and a firstfrequency at which one or more photons of the surface acoustic wavesignal resonate.
 3. The method of claim 1, further comprising:transferring, by the microwave Josephson mixer, quantum information fromthe superconducting microwave resonator to the superconducting surfaceacoustic wave resonator based on an application of a pump drive appliedat a frequency difference between a first frequency at which one or morephotons of the surface acoustic wave signal resonate and a secondfrequency at which one or more photons of the microwave signal resonate.4. The method of claim 1, further comprising: transferring, based on themicrowave control signal received by the microwave Josephson mixer,first quantum information from the superconducting surface acoustic waveresonator to the superconducting microwave resonator and second quantuminformation from the superconducting microwave resonator to thesuperconducting surface acoustic wave resonator.
 5. The method of claim1, further comprising: disconnecting, by the microwave Josephson mixer,a connection between the superconducting surface acoustic wave resonatorand the superconducting microwave resonator based on determining thatthe mixing of the surface acoustic wave signal and the microwave signalis to be stopped.
 6. The method of claim 5, further comprising:reenabling, by the microwave Josephson mixer, the connection between thesuperconducting surface acoustic wave resonator and the superconductingmicrowave resonator based on determining that the mixing of the surfaceacoustic wave signal and the microwave signal is to be restarted.
 7. Themethod of claim 1, further comprising: transferring, by the microwaveJosephson mixer, a first portion of quantum information between thesuperconducting surface acoustic wave resonator and the superconductingmicrowave resonator based on a first power of the microwave controlsignal; and transferring, by the microwave Josephson mixer, a secondportion of quantum information between the superconducting surfaceacoustic wave resonator and the superconducting microwave resonatorbased on a second power of the microwave control signal.
 8. The methodof claim 1, wherein the mixing the surface acoustic wave signal and themicrowave signal comprises transducing information carried by thesurface acoustic wave signal into the microwave signal in a unitarymanner.
 9. The method of claim 1, wherein the mixing the surfaceacoustic wave signal and the microwave signal comprises transducinginformation carried by the microwave signal into the surface acousticwave signal in a unitary manner.
 10. A method, comprising: implementing,by a frequency converter, a lossless frequency conversion between firstinformation of a superconducting surface acoustic wave resonator andsecond information of a superconducting microwave resonator based on apump signal received from a microwave source.
 11. The method of claim10, wherein the implementing the lossless frequency conversioncomprises: mapping, by the frequency converter, a propagating radiofrequency signal to a phononic mode in the superconducting surfaceacoustic wave resonator; and upconverting, by the frequency converter,the phononic mode to a photonic mode in the superconducting microwaveresonator via an application of a microwave control signal with adefined frequency, wherein the upconverting of the phononic mode isenabled by a lossless three-wave mixing interaction, and wherein anupconverted microwave signal propagates upon leaving the superconductingmicrowave resonator.
 12. The method of claim 11, wherein a first valueof a microwave control signal frequency is equal to an absolute value ofa frequency difference between a resonance frequency of thesuperconducting microwave resonator and the superconducting surfaceacoustic wave resonator.
 13. The method of claim 10, wherein theimplementing the lossless frequency conversion comprises: mapping, bythe frequency converter, a propagating microwave frequency signal to aphotonic mode in the superconducting microwave resonator; anddownconverting, by the frequency converter, the photonic mode to aphononic mode in the superconducting surface acoustic wave resonator viaan application of a microwave control signal with a defined frequency,wherein the downconverting of the photonic mode is enabled by a losslessthree-wave mixing interaction, and wherein a downconverted surfaceacoustic wave signal propagates upon leaving the superconducting surfaceacoustic wave resonator.
 14. The method of claim 10, further comprising:transferring, by the frequency converter, information from thesuperconducting surface acoustic wave resonator to the superconductingmicrowave resonator based on a frequency and an amplitude of a microwavecontrol signal.
 15. The method of claim 14, wherein the informationcomprises quantum information.
 16. The method of claim 10, furthercomprising: transferring, by the frequency converter, information fromthe superconducting microwave resonator to the superconducting surfaceacoustic wave resonator based on a frequency and an amplitude of amicrowave control signal.
 17. A method, comprising: inputting, by anentanglement component, a first input signal that comprises a firstfrequency into a superconducting surface acoustic wave resonator;inputting, by the entanglement component a second input signal thatcomprises a second frequency into a superconducting microwave resonator;and outputting, by the entanglement component, an output signal thatcomprises an entangled signal that comprises an amplified superpositionof input fields entering the superconducting surface acoustic waveresonator and the superconducting microwave resonator.
 18. The method ofclaim 17, wherein a first qubit is operatively coupled to theentanglement component via the superconducting surface acoustic waveresonator, and wherein a second qubit is operatively coupled to theentanglement component via the superconducting microwave resonator. 19.The method of claim 17, further comprising: generating, by theentanglement component, the entangled signal between one or more phononsof a surface acoustic wave output by the superconducting surfaceacoustic wave resonator and one or more microwave photons output by thesuperconducting microwave resonator.
 20. The method of claim 17, whereinthe entangled signal comprises an entanglement between a phononic modeand a photonic mode.
 21. A superconducting device, comprising: a firstsuperconducting qubit coupled to a superconducting surface acoustic waveresonator; a second superconducting qubit coupled to a superconductingmicrowave resonator; and a Josephson ring modulator coupled to thesuperconducting surface acoustic wave resonator and the superconductingmicrowave resonator.
 22. The superconducting device of claim 21, whereinthe first superconducting qubit is capacitively coupled to thesuperconducting surface acoustic wave resonator and wherein the secondsuperconducting qubit is capacitively coupled to the superconductingmicrowave resonator.
 23. The superconducting device of claim 22, furthercomprising: a pump drive operatively coupled to two adjacent nodes ofthe Josephson ring modulator via a first coupling capacitor and via asecond coupling capacitor.